Practice question

Without prey or another usable food source, predator intake falls to zero while metabolic maintenance, mortality, and emigration continue. In the Lotka–Volterra equation dP/dt = baNP − mP, setting prey density N to zero gives dP/dt = −mP. Predator abundance then declines exponentially at rate m, assuming a closed population and no immigration. Stabilization would require replacement of deaths through feeding-supported reproduction or external subsidy, while increase is impossible under the model because prey conversion supplies the positive growth term. Oscillation also requires reciprocal feedback between both populations and cannot continue when one is absent. Real predators may persist temporarily on stored reserves, enter dormancy, migrate, scavenge, or switch to alternative prey, so “absence of prey” must mean absence of all effective food. Those mechanisms change the model assumptions rather than the basic energetic conclusion. The population-level decline arises from the balance of births and deaths, not because every individual dies immediately when prey disappear.